Abilio Rodrigues

Federal University of Minas Gerais | UFMG · Departamento de Filosofia

The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules of propagation of classicality, which are inferences that express how the classicality operator \circ is tran...

In this paper I discuss two claims made by Priest in \textit{Some Comments and Replies} (DOI: 10.1007/978-3-030-25365-3\_27, 2019): (i) that the idea of `contradictions in reality' lacks textual support in his work, and (ii) that such contradictions would require a theory of truth as correspondence with entities such as facts or states of affairs...

The main aim of this paper is to introduce the logics of evidence and truth \(LET_{K}^+\) and \(LET_{F}^+\) together with sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics \(LET_{K}\) and \(LET_{F}^-\) with rules of propagation of classicality, which are inferences that express how the classi...

The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with sound, complete, and decidable 6-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules of propagation of classicality, which are inferences that express how the classicality operator o is transmitted...

This chapter gathers together and sums up the recent work on technical and philosophical aspects of logics of evidence and truth (LETs) through a study of the logics LETF and LETK, including an application of the latter to the problem of abduction. LETF is a paracomplete and paraconsistent sentential logic equipped with a unary operator ∘ that divi...

The main aim of this paper is to introduce first-order versions of logics of evidence and truth, together with corresponding sound and complete Kripke semantics with variable and constant domains. According to the intuitive interpretation proposed here, these logics intend to represent possibly inconsistent and incomplete information bases over tim...

This paper introduces the logic QLETF, a quantified extension of the logic of evidence and truth LETF, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LETF is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ a...

The main aim of this paper is to introduce first-order versions of logics of evidence and truth, together with corresponding sound and complete Kripke semantics with variable and constant domains. According to the intuitive interpretation proposed here, these logics intend to represent possibly inconsistent and incomplete information bases over tim...

The aim of this text is to reply to criticisms of the logics of evidence and truth and the epistemic approach to paraconsistency advanced by Barrio [2018], and Lo Guercio and Szmuc [2018]. We also clarify the notion of evidence that underlies the intended interpretation of these logics and is a central point of Barrio’s and Lo Guercio & Szmuc’s cri...

This draft contains proofs of adequacy results for natural deduction systems for the first-order logics QFDE, QLP, QK3, N− , NP, and N with respect to Kripke semantics with variable domains.

This paper introduces the logic of evidence and truth \({ LET}_{F}\) as an extension of the Belnap–Dunn four-valued logic \({ FDE}\). \({ LET}_{F}\) is a slightly modified version of the logic \({ LET}_{J}\), presented in Carnielli and Rodrigues (Synthese 196:3789–3813, 2017). While \({ LET}_{J}\) is equipped only with a classicality operator \({\c...

This paper introduces the logic QLETF, a quantified extension of the logic of evidence and truth LETF, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LETF is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ○ a...

Essay Review: Paraconsistent Logic: Consistency, Contradiction and Negation: Walter Carnielli and Marcelo E. Coniglio, New York, Springer International Publishing, 2016, xxiv + 398 pp., US$109.99 (pbk) ISBN-13: 978-3319814537

This paper presents a sound, complete, and decidable analytic tableau system for the logic of evidence and truth LETF, introduced in Rodrigues, Bueno-Soler \& Carnielli (Synthese, DOI: 10.1007/s11229-020-02571-w, 2020). LETF is an extension of the logic of first-degree entailment (FDE), also known as Belnap-Dunn logic. FDE is a widely studied fou...

The aim of this text is to reply to criticisms of logics of evidence and truth and the epistemic approach to paraconsistency advanced by Barrio (Principia 22:87-112, 2018) and Lo Guercio & Szmuc (Principia 22:153-170, 2018). We also clarify the notion of evidence that underlies the logics of evidence and truth and is a central point in Barrio's an...

Neste texto, apresentamos duas abordagens distintas, mas não necessariamente excludentes, da paraconsistência. A primeira trata das lógicas da evidência e verdade (logics of evidence and truth), nas quais contradições são interpretadas como evidência não conclusiva, simultânea e conflitante para um par de proposições A e ¬A. A segunda abordagem pro...

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics o...

Neste texto, apresentamos duas abordagens não dialeteístas da paraconsistência, discutindo as principais motivações e os conceitos básicos de algumas lógicas paraconsistentes. A primeira abordagem trata das lógicas da evidência e verdade (logics of evidence and truth), nas quais contradições são interpretadas como evidência não conclusiva, simultân...

In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N4 and the logic of first-degreeentailment (FDE) with a classicality operator that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these model...

The aim of this text is to show that the account of logical pluralism presented by Beall and Restall (Logical Pluralism, OUP, 2006) falls short of providing an adequate account of different contexts with different logics, particularly with respect to paraconsistent logics. We also argue that the interpretation of paraconsistency in terms of conflic...

From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic logic) lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle...

The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The pape...

Proof-theoretic semantics provides meanings to the connectives of intuitionistic logic without the need of a semantics in the standard sense of an attribution of semantic values to formulas. Meanings are given by the inference rules that, in this case, do not express preservation of truth but rather preservation of availability of a constructive pr...

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics...

The formal system proposed by Heyting (1930, 1956) became the standard formulation of intuitionistic logic. The inference called ex falso quodlibet, or the principle of explosion, according to which anything follows from a contradiction, holds in intuitionistic logic. However, it is not clear that explosion is in accordance with Brouwer's views on...

From the technical point of view, naturally philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic logic) lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and exclu...

The aim of this paper is to show that Frege's argument which concluded that the reference of a sentence is its truth-value, presented in On Sense and Reference (1892), can be reconstructed taking into account the problems of the notion of conceptual content presented in the Begriffsschrift (1879) and also other passages from a letter to Russell (19...

Proof-theoretic semantics provides meanings to the connectives of intuitionistic logic without the need for a semantics in the standard sense of an attribution of semantic values to formulas. Meanings are given by the inference rules that, in this case, do not express preservation of truth but rather preservation of availability of a constructive p...

Foreword : Consistency, Contradiction, and Consequence

Resumo: O objetivo deste texto é apresentar um breve relato de como contradições e o princípio da explosão foram pensados no decorrer da história da filosofia, da formulação aristotélica do princípio da não contradição até a paraconsistência contemporânea, passando pela formulação do princípio da explosão na Idade Média e pela discussão sobre contr...

There are two foundational but not properly developed ideas in da Costa's approach to paraconsistency: the 'well-behavedness' operator and the duality between paraconsistent and intuitionistic logics. The aim of this paper is to present how these two ideas can be developed by Logics of Formal Inconsistency (LFIs) and Logics of Formal Undeterminedne...

This chapter proposes a study of philosophical and technical aspects of logics of formal inconsistency (LFI s), a family of paraconsistent logics that have resources to express the notion of consistency inside the object language. This proposal starts by presenting an epistemic approach to paraconsistency according to which the acceptance of a pair...

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LETJ ), designed to deal, respectively, with evidence and with evidence and truth....

The aim of this text is to present the philosophical motivations for the logics of formal inconsistency (LFIs), along with some relevant technical results. The text is divided into two main parts (besides a short introduction). In the section 2, we shall present and discuss philosophical issues related to paraconsistency in general, and especially...

The purpose of this short essay is to explain the role of contradictions in the development of scientific theories. We argue that contradictions are not to be seen as a signal of defeat, but overall as a chance for improvement.

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view a...

The aim of this text is to present the philosophical motivations for the Logics of Formal Inconsistency (LFIs), along with some relevant technical results. The text is divided into two main parts (besides a short introduction). In Sect. 3.2, we present and discuss philosophical issues related to paraconsistency in general, and especially to logics...

O objetivo do texto e apresentar um panorama da atual discussao sobre fazedoresde- verdade. Sera dada enfase na caracterizacao da relacao de fazer-verdadeiro e no problema dos fazedores-de-verdade de proposicoes universais e negacoes.

Resumo: O objetivo deste artigo é apresentar e analisar o chamado mo-nismo de fazedores-de-verdade, um resultado segundo o qual qualquer faze-dor-de-verdade faz verdadeira qualquer proposição verdadeira. Esse re-sultado, que trivializa a noção de fazedores-de-verdade, depende da ca-racterização da relação de fazer-verdadeiro em termos de implicação...